Ondrouch Jan: Technická mechanika - Vysoká Å¡kola báÅská ...
Ondrouch Jan: Technická mechanika - Vysoká Å¡kola báÅská ...
Ondrouch Jan: Technická mechanika - Vysoká Å¡kola báÅská ...
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T E C H N I C K Á M E C H A N I K A<br />
───────────────────────────────────────────────────<br />
k L<br />
Im<br />
r<br />
σ ρ<br />
Trajektorie<br />
j ϕ<br />
L<br />
i ρ<br />
iϕ<br />
r = ρ⋅e<br />
= −1<br />
i (6.14)<br />
kde ρ = ρ(t) a φ = φ(t) jsou parametrické<br />
r<br />
rovnice dráhy.<br />
θ φ<br />
ρ<br />
•<br />
φ<br />
0<br />
Re<br />
r<br />
Obr. 6.8<br />
Rychlost<br />
⋅<br />
dr ⎛ ⋅ ⋅ ⎞<br />
⎜ ⎟ iϕ<br />
v = = r =<br />
ρ+ i⋅ρ⋅ϕ<br />
⋅e<br />
= v ρ ⋅iρ<br />
+ v ϕ ⋅ jϕ<br />
dt ⎝ ⎠<br />
(6.15)<br />
kde<br />
⋅<br />
v ρ = ρ ,<br />
⋅<br />
ϕ = ρ⋅ϕ<br />
v a velikost rychlosti (obr. 6.9)<br />
v ϕ<br />
v<br />
vρ<br />
v =<br />
ρ<br />
⋅<br />
2<br />
⎛ ⋅ ⎞<br />
+ ⎜ ⎟<br />
ρ⋅ϕ<br />
⎝ ⎠<br />
2<br />
•<br />
Obr. 6.9<br />
Zrychlení<br />
⋅ ⎡⎛<br />
⋅⋅ ⋅ ⎞ ⋅⋅ ⋅ ⋅ ⎤<br />
⎢⎜<br />
2 ⎟ ⎛ ⎞<br />
⎜ ⎟⎥<br />
iϕ<br />
a = v = ρ− ρ⋅ϕ + i⋅<br />
⋅ = ρ ⋅ ρ + ϕ ⋅ ϕ<br />
⎢<br />
ρ⋅ϕ+ 2⋅ρ⋅ϕ<br />
⎜ ⎟<br />
e a i a j<br />
⎥<br />
⎣⎝<br />
⎠ ⎝ ⎠⎦<br />
(6.17)<br />
kde<br />
⋅⋅ ⋅<br />
2<br />
a ρ = ρ− ρ⋅ϕ<br />
,<br />
⋅⋅ ⋅ ⋅<br />
a ϕ = ρ⋅ϕ+ 2 ρ⋅ ϕ a velikost zrychlení (obr. 6.10)<br />
a ϕ<br />
a<br />
•<br />
a ρ<br />
2<br />
2<br />
⎛ ⋅⋅ ⋅ ⎞<br />
2 ⎛ ⋅ ⋅ ⎞<br />
a =<br />
⎜<br />
ρ− ρ⋅ϕ<br />
⎟<br />
+ ⎜2<br />
⎟<br />
ρ⋅ϕ<br />
⎜ ⎟<br />
(6.18)<br />
⎝ ⎠ ⎝ ⎠<br />
Obr. 6.10<br />
41
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